Study of the influence of boundary conditions on the dynamics of a gas suspension with a viscous carrier medium in the channel

Abstract

This paper presents a numerical model of the propagation of a shock wave from a homogeneous gas into a gas suspension — a suspension of dispersed particles in a gas. This topic is relevant in connection with various industrial applications. The carrier medium is described as a viscous compressible heat-conducting gas. The mathematical model implemented a continuum technique for modeling the dynamics of inhomogeneous media — for each of the components of the mixture, the complete hydrodynamic system of equations of motion was solved, and the exchange of momentum and heat exchange between the components of the mixture was taken into account. The system of equations for the dynamics of the carrier medium and dispersed phase includes equations of density continuity, conservation equations for the spatial components of the momentum of the carrier and dispersed phase, and energy conservation equations. For the dispersed phase, the concept of average density is introduced — the product of the volumetric content and the physical density of the material. Volume content is a function of time and space variables; the physical density of a material is a constant. The equations of the mathematical model were solved using the explicit McCormack finite-difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Two types of boundary conditions in the channel were considered: homogeneous Neumann boundary conditions on the side surfaces of the channel and homogeneous Dirichlet boundary conditions. A gas suspension with finely dispersed particles and a large volumetric content of the dispersed phase was considered, so the parameters of the gas suspension are such that the dispersed phase has a significant impact on the dynamics of the carrier medium. It has been revealed that in the case of homogeneous Neumann boundary conditions, the disturbance through the gas suspension propagates faster, and the two-dimensional distribution of the velocity modulus of the carrier medium is uniform. When homogeneous Dirichlet boundary conditions are specified, the velocity modulus has a parabolic profile and a larger value; the disturbance propagates through the medium at a lower speed than the disturbance propagating through the channel with homogeneous Neumann boundary conditions. The results obtained can be used in modeling gas flows.